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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Linking Game-Theoretical Approaches with Constructive Type Theory: Dialogical Strategies, CTT Demonstrations and the Axiom of Choice

Linking Game-Theoretical Approaches with Constructive Type Theory: Dialogical Strategies, CTT Demonstrations and the Axiom of Choice

Clerbout, Nicolas
Rahman, Shahid

Paperback

Series: Springerbriefs in Philosophy

FictionGeneral MathematicsLogic

ISBN10: 3319190628
ISBN13: 9783319190624
Publisher: Springer
Published: Jul 21 2015
Pages: 99
Weight: 0.41
Height: 0.26 Width: 6.14 Depth: 9.21
Language: English
This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work's subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

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